How to find zeros of a function?

Question

Wenjie 2018-12-17

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评论： DAVID 2024-9-20，2:55

For instance,

x = -3.55:0.1:3.55;

y = x.^2 - 4;

Obviously, when x=2 or -2, y=0.

But I want to know how to use matlab to find zeros of a function y = f(x) when x is a matrix defined by the user like the above case.

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Mark Sherstan 2018-12-17

As per documentaiton note:

x = fzero(fun,x0) tries to find a point x where fun(x) = 0. This solution is where fun(x) changes sign—fzero cannot find a root of a function such as x^2.

Akira Agata 2018-12-17

If your function is always polynomial, you can use roots function to do this task. Please look at the following help page.

https://www.mathworks.com/help/matlab/ref/roots.html

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Answer 1

Wenjie 2018-12-17

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在 MATLAB Online 中打开

I've found the solution. First, define the function in a separate file as

function y = fun(x)
y = x.^2-4;
end

Then use fzero to find x value that will give y=0.

x0 = fzero(@(x) fun(x), 3)

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Nico 2024-2-25

What does the @(x) and the 3 mean? Sorry I'm university student with no experience...

Dyuman Joshi 2024-2-25

编辑：Dyuman Joshi 2024-2-25

@(x) is the syntax used to define a Function Handle / Anonymous Functions

The 3 is provided as an initial guess for fzero() to work with - see fzero for more information.

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Answer 2

Alexander 2024-2-25

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https://ww2.mathworks.cn/matlabcentral/answers/436065-how-to-find-zeros-of-a-function#answer_1416123

在 MATLAB Online 中打开

If it's not a function but meassured data I would go like this in a first try:

x = -3.55:0.0001:3.55; % assuming 10 kHz sample frequency
y = x.^2 - 4;
yS = sign(y);
dyS = diff(yS);
Z=find(dyS ~= 0);
x(Z)

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DAVID 2024-9-20，2:55

This was really elegant, thanks!

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Answer 3

Walter Roberson 2018-12-17

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x(y==0)

Note that this can miss an indefinite number of zeroes of a function if the x do not happen to sample at the right places . It also will not detect zero crossings between x values . You could make use of the results to get hints about zero crossings .